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Chapter 1: Problem 13

In each term, give the numerical coefficient of the variable(s). See Objective 2. $$ -12 k $$

Short Answer

Expert verified
-12

Step by step solution

01

Identify the Term

Focus on the term provided, which is \(-12k\).
02

Locate the Variable

In the term \(-12k\), the variable is \(k\).
03

Extract the Numerical Coefficient

The numerical coefficient is the number that multiplies the variable \(k\). In this case, it is \( -12\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Variables
In algebra, variables are symbols that represent numbers or values. They are usually denoted by letters like \(x\), \(y\), or in our case, \(k\). They can take on different values, which allows us to create general formulas and equations. By giving variables specific values, we can solve these equations and find answers to real-world problems. For example, in science, variables can represent physical quantities like speed or distance. Understanding variables is crucial for working with algebraic expressions.
Terms
A term in algebra is a single mathematical expression. It can be a number, a variable, or a combination of both. Consider the expression \(-12k\). This is a term because it combines the number \(-12\) and the variable \(k\). In any term:
  • The numerical part is called the coefficient.
  • The variable part represents the unknown.
Terms are separated by plus or minus signs in an equation. For instance, in the expression \(4x - 3y + 7\), there are three terms: \(4x\), \(-3y\), and \(7\). Recognizing and understanding terms is fundamental in algebra.
Algebra
Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. These symbols (like variables) stand for numbers and allow us to create equations and formulas. Algebra helps us understand relationships between different quantities and solve equations by finding the values of unknown variables. For instance, a simple equation like \(2x + 3 = 7\) can be solved to find that \(x = 2\). In advanced applications, algebra is used in fields like engineering, economics, and computer science to model and solve complex problems. Knowing algebra is essential for success in many areas of higher education and professional work.

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Most popular questions from this chapter

Write a numerical expression for each phrase and simplify. \(-2\) added to the sum of \(-18\) and 11

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